Sigh. Let's make sure I am clear in what I am claiming. I am saying that, for a given (fixed) speed, a shorter stride can be less efficient than a longer stride.
(sigh, just when you thought it was safe to go back in the water, lol) I understand that and I'm saying just the opposite, based on plenty of experience and also overwhelming amounts of advice and experienced-based testimony from god knows how many runners who have improved their running form by increasing their cadence and shortening their stride.
You're talking from a purely analytical, theoretical, numbers standpoint but not saying much about the real world. I suspect your formula might be true when a runner tips the scale into the ad absurdum range of turnover rate, but for most of us, a bump-up in cadence has a positive effect. This has been true for decades, which, again, is why I keep coming backl to this theory of yours.
I can't relate directly to your 3m/s and fractions as measurements because, well, nobody can. Talk in terms of turnover rate, like I tried to do in an earlier post.
Ask me instead: Do you honestly feel that going from a 165 turnover rate at a given pace to 185 will increase your efficieny?
And I'll answer: hells yeah I do. I know it does because I've done it and have only benefited from the change. As I believe Olle mentioned earlier, shortening the stride has a positive effect on reducing (energy-wasting) vertical movement (among many other benefits that I don't think your formulas take into account). So, it may well work out paper the way you say, but human biomechanics/physiology are lot more complex than that.
Anyway, the reason I came back to this thread is because I was thinking about this study the other day while running. I was wondering if the drop in efficiency noted in the "barefoot" sessions may well have simply come from the runners not being as relaxed running on the treadmill as when they were wearing the Mayflys. It could be very possible that they were tensed up and not allowing the feet to relax. All muscle usage is reflected in the testing equipment, it doesn't matter where the effort is specifically going.